There are no plans to support this resolution. In practice, it would offer no advantage over 2880x720; the 4 picolitre drops are plenty large enough to create solid density at 2880x720 DPI, and packing more resolution in already high resolution dimension isn't going to achieve any visible improvement. If you want to try 2880x1440 (which would at least give you more vertical resolution), you can try using the Epson 925 driver.
If you really want higher resolution, get the 960, which offers 2880x1440 with 2 picolitre drops; this really does offer visible improvement over the 820, but even on that printer there's awfully little difference in output quality between 2880x1440 and 1440x720, which is the next resolution choice. However, both the 780 and 820 are base model 6-color printers; there's no reason to do this as an "upgrade". The printer may not be doing 5760x720dpi in hardware anyway.
The Epson web site always refers to "5760x720 optimized DPI"; there is no explanation as to what " ... more.
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